STAT 110, Notes for Week 8/23/16
STAT 110, Notes for Week 8/23/16 STAT 110
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This 4 page Class Notes was uploaded by runnergal on Saturday August 27, 2016. The Class Notes belongs to STAT 110 at University of South Carolina taught by Dr. Wilma J. Sims in Fall 2016. Since its upload, it has received 9 views. For similar materials see Introduction to Statistical Reasoning in Statistics at University of South Carolina.
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Date Created: 08/27/16
STAT 110 – Notes for Week of 8/23/16 Chapter 2 o When collecting data, the sample should represent the population since it is selected from the population. o Bias: when data is consistently skewed in one direction. Personal choice inevitably produces bias. o Some sampling designs are biased by nature; they include: Convenience Sampling: when the sample that is chosen from the population is comprised of individuals that are the easiest to reach. One example is if I was surveying popular USC graduation photo locations and I only looked at my friends’ photos instead of a more diverse sample of USC students’ photos. Voluntary Response Sampling: when the sample that is chosen from the population is comprised of individuals that volunteer to participate in the study. One example is a call-in survey on a radio station. If the listeners are mostly conservative, then the survey will be biased in favor of conservatism. These sampling designs are also known as haphazard sampling techniques. o To avoid bias, researchers often use simple random samples (SRS): where individuals in the population each have an equal chance of be chosen for the sample. o These samples are often selected using random digits: a string of random digits that can be used to select individuals, provided that each individual is labeled as a number. An example of a table of random digits can be found in the back of your textbook. These number labels can be assigned in any order (or no order at all) as long as each individual receives a number. If you encounter a number greater than any of your labels in a table of random digits, skip it and move onto the next number. Lines, columns, and groups have no meaning in a table of random digits; simply read the digits in order. Chapter 3 o Parameter: a number that describes a population. Researchers usually do not know the number of individuals in a population and therefore cannot find this number, hence why they take samples. For example, “100% of the students in this class take statistics” is a parameter. o Statistic: a number that describes the sample. This number may change from sample to sample, since there are different individuals in each sample. In a good survey, however, there should not be large changes in this number. For example, “40% of all individuals in this class are freshmen” is a statistic. o A proportion (p) is an unknown parameter. Since we don’t know the proportion, we must take a sample proportion (p-hat). (It can also look like a p with a carrot over it.) o n = number of individuals in the sample. o p-hat = (number of favorable outcomes/successes)/n For example, if I wanted to know how many freshmen were in this class, I would do the research and find out that 80 freshmen were in this class of 200. Therefore, p-hat = 80/200. P-hat is 40%. All proportions fall between 0-1, since they are all percentages. Researchers estimate the value of p based on p-hat. o Sometimes errors occur in these surveys. Two types of error are: Bias: when data is consistently skewed in one direction. Bias can be reduced by using simple random samples (SRSs). For example, the real proportion of the freshmen in this class is 40%. If I conducted several surveys and got proportions of 55%, 57%, 54%, and 56%, the data would be biased in favor of the freshmen. The survey results could not be trusted. Variability: when different data samples give vastly different proportions. Variability can be reduced by using larger samples. For example, the real proportion of the freshmen in this class is 40%. If I conducted multiple surveys and got proportions of 40%, 60%, 20%, and 0%, I would have a lot of variability. None of the survey results could be trusted. A good survey has low bias and low variability. o Many statistics will include a margin of error: plus or minus a percentage (ex. 2%) the researchers believe the proportion may deviate from. Margins of error increase the range that the researchers believe the parameter falls within. To find out the margin of error with 95% confidence for a simple random sample, just do 1/(√????). o A statistic may also include a confidence statement: a sentence that uses a margin of error to indicate how sure the researchers are that the parameter falls within the range. Confidence statement formula: We are 95% confident that the actual percentage of the population with this characteristic is between x% and y%. You fill in the underlined parts! x is the percentage you get when you subtract the margin of error from your proportion, and y is the percentage you get when you add the margin of error to your proportion. Your proportion should be in the exact middle of those numbers. Confidence statements always apply to the population, since we are always sure what the proportion of the sample is. Confidence statements are never completely certain; unforeseen variables may influence the data without the researchers’ knowledge. Increasing the sample size decreases the margin of error, but increasing the population does not.